Mary is making some shirts for her school's drama department. The fabric store has $3 \frac{1}{6}$ yards of the fabric she wants in stock, but this quantity of fabric can make only $1 \frac{1}{2}$ shirts. What length of fabric does Mary need to buy if she wants to sew $2 \frac{1}{4}$ shirts?
A. $1 \frac{1}{6}$ yards
B. $4 \frac{3}{4}$ yards
C. $2 \frac{3}{8}$ yards
D. $3 \frac{5}{6}$ yards
Answer (2)
Convert the mixed number 3 6 1 to an improper fraction: 6 19 .
Multiply the improper fraction by 2: 2 × 6 19 = 6 38 .
Simplify the fraction: 6 38 = 3 19 .
Convert the improper fraction back to a mixed number: 3 19 = 6 3 1 .
6 3 1
Explanation
Understanding the Problem We are given that Mary needs to make shirts for her school's drama department. The fabric store has 3 6 1 yards of fabric, which is enough to make 1 shirt. We need to find out how much fabric Mary needs to buy to make 2 shirts.
Finding the Total Fabric Needed Since 3 6 1 yards of fabric is needed for 1 shirt, we need to multiply this amount by 2 to find the amount of fabric needed for 2 shirts.
Converting to Improper Fraction First, convert the mixed number 3 6 1 to an improper fraction: 3 6 1 = 6 3 × 6 + 1 = 6 18 + 1 = 6 19 So, we need 6 19 yards of fabric for 1 shirt.
Multiplying by 2 Now, multiply the amount of fabric needed for 1 shirt by 2 to find the amount of fabric needed for 2 shirts: 2 × 6 19 = 6 2 × 19 = 6 38 Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2: 6 38 = 6 ÷ 2 38 ÷ 2 = 3 19
Converting Back to Mixed Number Convert the improper fraction 3 19 back to a mixed number: 3 19 = 6 3 1 So, Mary needs 6 3 1 yards of fabric to make 2 shirts.
Final Answer Therefore, Mary needs 6 3 1 yards of fabric to make 2 shirts.
Examples
If you're planning a garden and know that one packet of seeds covers 3 6 1 square feet, you can use this same math to figure out how many square feet two packets will cover. This helps in planning how much space you need for your plants. Similarly, if a recipe calls for 3 6 1 cups of flour and you want to double the recipe, you'd need to calculate 2 × 3 6 1 to find out how much flour you need, which is 6 3 1 cups.
Mary needs to buy 4 4 3 yards of fabric to sew 2 4 1 shirts. This is calculated by first determining how much fabric is needed per shirt and then multiplying that by the number of shirts she wants to make. Therefore, the chosen option is B.
;
